How many Integers

Number Theory Level pending

How many integers n n (including negative integers) are such that 15 − n 3 − n \dfrac{15-n}{3-n} is an integer?

11 12 10 8 9

Venkatachalam J by Venkatachalam J , 43, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

15 − n 3 − n = 1 + 12 3 − n \dfrac{15-n}{3-n}=1+\dfrac{12}{3-n} . Now, 12 12 has 6 6 positive factors. Therefore the total number of the values of n n is 2 × 6 = 12 2\times 6=\boxed {12} .

1 Helpful 0 Interesting 3 Brilliant 0 Confused

Brilliant!

Mahdi Raza - 1 year, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...